The subject invention relates to the analysis of data obtained during the measurement of periodic structures on semiconductors. In particular, an approach is disclosed which allows accurate, real time analysis of such structures.
The semiconductor industry is continually reducing the size of features on wafers. These features include raised profiles and trenches that have a particular height (or depth), width and shape (contour). Accurate measurement of these features is necessary to insure appropriate yields.
Technologies suitable for measuring these small periodic features (critical dimensions) are quite limited. Optical measurement technology is the most desirable since it is a non-contact technique. However, the smallest spot size of conventional optical probe beams is larger than the size of the periodic features which need to be measured.
FIG. 1 illustrates a substrate 8 having basic periodic pattern 10 formed thereon. The pattern will have a certain characteristic height (H), separation (S) and width (W). Note that in this illustration, the side walls of the structure are not vertical, so the width varies over the height of the structure. FIG. 1 also schematically indicates a probe beam spot 12 which is larger than the spacing between the individual features.
The difficulty in directly measuring such small structures has lead to the development of scatterometry techniques. These techniques have in common the fact that light reflected from the periodic structure is scattered and can be treated mathematically as light scattered from a grating. A significant effort has been made to develop metrology devices that measure and analyze light scattered from a sample in order to evaluate the periodic structure.
For example, U.S. Pat. No. 5,607,800 discloses the concept of measuring reflected (scattered) light created when a broad band probe beam interacts with a sample. The reflected light intensity as a function of wavelength is recorded for a number of reference samples having known periodic features. A test sample is then measured in a similar manner and the output is compared to the output obtained from the reference samples. The reference sample which had the closest match in optical response to the test sample would be assumed to have a periodic structure similar to the test sample.
A related approach is disclosed in U.S. Pat. No. 5,739,909. In this system, measurements from a spectroscopic ellipsometer are used to characterize periodic structures. In this approach, the change in polarization state as a function of wavelength is recorded to derive information about the periodic structure.
Additional background is disclosed in U.S. Pat. No. 5,867,276. This patent describes some early efforts which included measuring the change in intensity of a probe beam as a function of angle of incidence. Measurements at multiple angles of incidence provide a plurality of separate data points. Multiple data points are necessary to evaluate a periodic structure using a fitting algorithm. In the past, systems which took measurements at multiple angles of incidence required moving the sample or optics to vary the angle of incidence of the probe beam. More recently, the assignee herein developed an approach for obtaining scatterometry measurements at multiple angles of incidence without moving the sample or the optics. This approach is described in U.S. Pat. No. 6,429,943, issued Aug. 6, 2002.
U.S. Pat. No. 5,867,276, like the other prior art discussed above, addresses the need to obtain multiple data points by taking measurements at multiple wavelengths. This patent is also of interest with respect to its discussion of analytical approaches to determining characteristics of the periodic structure based on the multiple wavelength measurements. In general, these approaches start with a theoretical model of a periodic structure having certain attributes, including width, height and profile. Using Maxwell""s equations, the response which a theoretical structure would exhibit to incident broadband light is calculated. A rigorous coupled wave theory can be used for this analysis. The results of this calculation are then compared to the measured data (actually, the normalized data). To the extent the results do not match, the theoretical model is modified and the theoretical data is calculated once again and compared to the measured data. This process is repeated iteratively until the correspondence between the calculated data and the measured data reaches an acceptable level of fitness. At this point, the characteristics of the theoretical model and the actual sample should be very similar.
The calculations discussed above are relatively complex even for the most simple models. As the models become more complex (particularly as the profiles of the walls of the features become more complex) the calculations become exceedingly long and complex. Even with todays high speed processors, the art has not developed a suitable approach for analyzing more complex structures to a highly detailed level on a real time basis. Analysis on a real time basis is very desirable so that manufacturers can immediately determine when a process is not operating correctly. The need is becoming more acute as the industry moves towards integrated metrology solutions wherein the metrology hardware is integrated directly with the process hardware.
One approach which allows a manufacturer to characterize features in real time is to create xe2x80x9clibrariesxe2x80x9d of intensity versus wavelength plots associated with a large number of theoretical structures. This type of approach is discussed in PCT application WO 99/45340, published Sep. 10, 1999 as well as the references cited therein. In this approach, a number of possible theoretical models are created in advance of the measurement by varying the characteristics of the periodic structure. The expected optical response is calculated for each of these different structures and stored in a memory to define a library of solutions. When the test data is obtained, it is compared to the library of stored solutions to determine the best fit.
While the use of libraries does permit a relatively quick analysis to be made after the sample has been measured, it is not entirely satisfactory for a number of reasons. For example, each time a new recipe is used (which can result from any change in structure, materials or process parameters), an entirely new library must be created. Further, each library generated is unique to the metrology tool used to make the measurements. If the metrology tool is altered in any way (i.e. by replacing an optical element that alters the measurement properties of the tool), a new library must be created. In addition, the accuracy of the results is limited by the number of models stored in the library. The more models that are stored, the more accurate the result, however, the longer it will take to create the library and the longer it will take to make the comparison. The most ideal solution would be to develop a system which permitted iterative (fitting) calculations to be performed in real time and which is easily modified to account for changes in the metrology tool and the process begin monitored.
One approach to speeding up the fitting calculation can be found in U.S. Pat. No. 5,963,329. (The latter patent and the other publications cited above are all incorporated herein by reference.) This patent discloses a method of reducing the number of parameters needed to characterize the shape or profile of the periodic structure. In this approach, the structure is mathematically represented as a series of stacked slabs. The authors suggest that the structure must be divided into bout 20 slabs to permit proper characterization of the structure. However, the authors note that performing an analysis with 40 variables (the width and height of 20 slabs) would be too computationally complex. Accordingly, the authors suggest reducing the complexity of the calculation by using sub-profiles and scaling factors. While such an approach achieves the goal of reducing computational complexity, it does so at the expense of limiting the accuracy of the analysis. Accordingly, it would be desirable to come up with an approach that was both highly accurate and could be performed on a real time basis.
To address this need, a system has been developed which permits the accurate evaluation of the characteristics of a periodic structure on a real time basis. In a first aspect of the subject invention, an improved analytical approach has been developed for increasing the efficiency of the calculations while maintaining a high degree of accuracy. In this aspect of the invention, a theoretical model of the structure is created. This initial model preferably has a single height and width defining a rectangular shape. Using Maxwell""s equations, the model""s response to the interaction with the probing radiation is calculated. The calculated response is compared with the measured result. Based on the comparison, the model parameters are iteratively modified to generate a rectangle, which would produce calculated data which most closely matches to the measured data.
Using this information, a new model is created with more than one width and more than one layer. Preferably, a trapezoid is created with three layers. The model parameters are then adjusted using a fitting algorithm to find the trapezoidal shape which would produce the theoretical data most closest to the measured data.
Using the results of this fitting process, the model is again changed, increasing the number of widths and layers. The fitting processes is repeated. The steps of adding widths and layers and fitting the model to the data are repeated until the level of fitness of the model reaches a predetermined level.
During these iterative steps, the thickness of the layers (density of the layers) are permitted to vary in a manner so that a higher density of layers will be placed in regions where the change in width is the greatest. In this way, the curvature of the side walls can be most accurately modeled.
In this approach, the number of widths and layers is not fixed. It might be possible to fully characterize a structure with only a few widths and layers. In practice, this method has been used to characterize relatively complex structures with an average 7 to 9 widths and 13 to 17 layers.
The scatterometry calculations associated with the early iterations of the models (square, trapezoid) are relatively simple and fast. However, as the number of widths and layers increase, the calculations become exponentially more difficult.
In order to be able to complete these calculations on a reasonable time scale, it was also necessary to develop a computing approach which minimized computational time. In another aspect of the subject invention, the scatterometry calculations are distributed among a group of parallel processors. In the preferred embodiment, the processor configuration includes a master processor and a plurality of slave processors. The master processor handles the control and the comparison functions. The calculation of the response of the theoretical sample to the interaction with the optical probe radiation is distributed by the master processor to itself and the slave processors.
For example, where the data is taken as a function of wavelength, the calculations are distributed as a function of wavelength. Thus, a first slave processor will use Maxwell""s equations to determine the expected intensity of light at selected ones of the measured wavelengths scattered from a given theoretical model. The other slave processors will carry out the same calculations at different wavelengths. Assuming there are five processors (one master and four slaves) and fifty wavelengths, each processor will perform ten such calculations to each iteration.
Once the calculations are complete, the master processor performs the best fit comparison between each of the calculated intensities and the measured normalized intensities. Based on this fit, the master processor will modify the parameters of the model as discussed above (changing the widths or layer thickness). The master processor will then distribute the calculations for the modified model to the slave processors. This sequence is repeated until a good fit is achieved.
This distributed processing approach can also be used with multiple angle of incidence information. In this situation, the calculations at each of the different angles of incidence can be distributed to the slave processor.
Further objects and advantages will become apparent with the following detailed description taken in conjunction with the drawings in which: